CN112152775A - Image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping and gene operation - Google Patents

Image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping and gene operation Download PDF

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CN112152775A
CN112152775A CN201910733890.XA CN201910733890A CN112152775A CN 112152775 A CN112152775 A CN 112152775A CN 201910733890 A CN201910733890 A CN 201910733890A CN 112152775 A CN112152775 A CN 112152775A
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刘羽
秦拯
胡娟
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention relates to an image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping and gene operation. The invention mainly comprises (1) providing a new two-dimensional Henon-Chebyshev chaotic system; (2) providing a gray level image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation; (3) a color image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation is provided.

Description

Image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping and gene operation
Technical Field
The invention relates to the field of information security and privacy protection, in particular to an image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping and gene operation.
Background
With the rapid development of network technology, people around the world can remotely transmit and share information. Information is available in many forms, such as text, images, and video. As a mainstream multimedia information type, images play an important role in daily information exchange due to their characteristics of intuition and rich information volume. Hundreds of millions of images per second are transmitted in the network, and once private information is leaked, the images pose serious threats to users, countries and even society. Therefore, it becomes increasingly important to ensure security of digital images in transmission.
To address these challenges, researchers have devised various encryption methods to protect the security of information in transmission. The core idea of encryption is to convert the information into an unrecognizable form so that it can be transmitted over a common channel and cannot be recovered to the original information without the key. Cryptography has a well-established architecture, and many excellent encryption algorithms have been proposed, such as DES, 3DES, IDEA, AES, and so on. However, these conventional encryption algorithms are mainly used for encrypting one-dimensional text information, and digital images have the characteristics of large data size, high redundancy, and strong correlation, and if these conventional algorithms are used for encrypting images, the time cost may be too high, so that it is difficult to meet the requirement of real-time processing. In addition, these conventional algorithms do not change the correlation between adjacent pixels of the image. Therefore, these conventional text encryption algorithms are not suitable for image encryption.
The chaotic system has the characteristics of pseudo-randomness, ergodicity, non-periodicity, high sensitivity to initial conditions and the like, and is widely used in cryptography to improve the security level of information. In addition, the chaotic system can generate chaotic sequences with any length, can meet the requirement of encrypting files with any size, and solves the problem of large image data volume. Therefore, researchers have designed various digital image encryption algorithms based on the chaotic system.
A good chaotic image encryption algorithm depends on two components: the first is chaotic system, and the second is encryption process. Many chaotic systems have been proposed, some of which are one-dimensional chaotic systems with simple structures and chaotic orbits, such as logical mapping, and some of which are high-dimensional chaotic systems with complex chaotic behaviors and orbits, such as 5D hyper-chaotic systems, 4D chaotic systems, and the like. One-dimensional chaotic systems may be vulnerable to brute force attacks, while high-dimensional chaotic systems have higher cost overhead and complex performance analysis. In the encryption process part, the conventional method usually has a scrambling and diffusion structure. The replacement stage mainly changes the relative position of the image pixels, and common replacement operations are point replacement, row-column replacement and the like. The diffusion stage mainly changes the value of the pixel, and common diffusion operations include exclusive-or operation at the pixel level, replacement at the bit level, diffusion operation, and the like.
In consideration of safety and implementation complexity, the invention provides a novel two-dimensional Henon-Chebyshev chaotic system which has better ergodicity, unpredictability and larger chaotic range compared with the original chaotic system. On the basis, the invention provides a gray image encryption method and a color image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation, and can realize good balance between safety and efficiency.
Disclosure of Invention
The present invention aims to solve the security problem in digital image transmission. Therefore, the invention provides an image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping and gene operation, which mainly comprises three contents:
1. a new two-dimensional Henon-Chebyshev chaotic system is provided;
2. providing a gray level image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation;
3. a color image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation is provided.
The specific contents are as follows:
1. a new two-dimensional Henon-Chebyshev chaotic system (2D-HCMM) is proposed. It is obtained by the cascade of Henon mapping and Chebyshev mapping, and is defined as follows:
Figure BDA0002162772560000031
where a, b, c ∈ R are system parameters. The modulo operation is performed to ensure that the output value is at [0,1 ]]Within the range of (1). Kinetic characteristics of 2D-HCMM were analyzed by phase diagram, bifurcation diagram, Lyapunov exponent and entropy of information. Compared with the original Henon mapping and Chebyshev mapping, the 2D-HCMM has better dynamic structure, better ergodicity and unpredictability, and the chaos range is expanded. The chaos range of the 2D-HCMM is a, c belongs to R,
Figure BDA0002162772560000032
and the larger the absolute value of b is, the better the chaotic behavior is.
2. A gray level image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation is provided.
As shown in the working flow chart of fig. 1, the gray image encryption method mainly comprises two parts, wherein the first part is a random sequence required in the encryption process generated by the two-dimensional Henon-Chebyshev chaotic system. The initial value of the system is updated with the hash value of the plaintext, so that the random sequence generated by the 2D-HCMM is different for different plaintexts. The second part is the image encryption process, which mainly adopts the methods of gene recombination and gene variation. The genetic recombinants now recombine the bit planes to disrupt the correlation between bit planes. Genetic variation is mainly realized by changing the original value of a random position on a binary bit plane into an opposite value, thereby achieving the purpose of changing the pixel value. For example, assuming that a certain pixel value of an 8-bit binary image is 14, its binary representation is 00011011, and when the value at the third position is changed to 00111011, its pixel value becomes 59. The positions of both recombination and mutation depend on the random sequence generated by the 2D-HCMM.
The detailed steps of the whole encryption process are as follows:
(1) setting keys { a, b, c, x10,y10,x20,y20T, calculating the original plaintext image Im×nThen dividing K into 32 blocks, each of size 8 bits, can be expressed as: k ═ K1,k2,k3,...,k32Wherein i ═ 1,2, 3.., 32, ki∈[0,255]。
(2) Updating the initial value of the 2D-HCMM system according to the following formula:
Figure BDA0002162772560000041
(3) extracting a plaintext image Im×nTwo of the 8 bit planes are selected to combine to form four complexesBit plane CP1,CP2,CP3,CP4。
I→I1,I2,I3,I4,I5,I6,I7,I8；
I1,I8→CP1；I2,I7→CP2；
I3,I6→CP3；I4,I5→CP4.
(4) Will compound the bit plane CP1,CP2,CP3,CP4Conversion to sequence, the gene recombination procedure was performed according to the following formula to obtain four new composite sequences:
Figure BDA0002162772560000042
wherein, u is mn/4, CPi(j)∈[0,22]Presentation sequence CPiThe jth element of (1); [ CP ]i(a),CPi(b)]Represents CPiThe set from the a-th element to the b-th element, CPa∪CPbIs a sequence CPaAnd CPbThe union of (a).
(5) Using updated System initial value x'10,y′10Iterating the 2D-HCMM system mn +1000 times, discarding the previous 1000 values to prevent transient effect, obtaining two sequences X and Y with the length of mn, and performing modular operation on X and Y respectively: x '═ Xmod 4, Y' ═ Ymod 4.
(6) According to a random sequence X' ═ { X ═1,x2,...,xmnAnd (5) carrying out gene mutation operation on the recombined composite sequence in the step (4):
Figure BDA0002162772560000051
wherein, CP1' (i) mutation indicates the sequence CP1The binary value of the i-th element of' (i) becomes an opposite value. For example, CP1′(i) The third element is 2, whose binary bit value is '10'; if CP1' (3) is mutated, which becomes the opposite value of '01 '. When the above steps are completed, the random sequence Y' ═ Y1,y2,...,ymnAnd fourthly, carrying out gene variation operation again to obtain four new variant sequences.
(7) Using updated System initial value x'20,y′20Iterating the 2D-HCMM system mn +1000 times, discarding the first 1000 values, and obtaining two random sequences S, R with the length mn. S, R are converted to three random sequences U, V, R' according to the following formula:
Figure BDA0002162772560000052
wherein Sort { S (a), S (b) } indicates that the a-th element to the b-th element in the sequence S are reordered in ascending order and obtain the index sequence thereof, and the index sequence indicates the position of the new element in the original sequence after the ordering.
(8) Rearranging the four variant sequences finally obtained in the step (6) into four matrixes CP with the size of m multiplied by n1″,CP2″,CP3″,CP4And then combined into an 8-bit matrix F:
F＝CP1″×20+CP2″×22+CP3″×24+CP4″×26
(9) performing row permutation on F through the sequence U to obtain a matrix FrThen through the sequence V to FrPerforming column permutation to obtain a matrix Frc。
(10) Will matrix FrcMorphed into a sequence, the following diffusion process is performed:
Figure BDA0002162772560000053
wherein
Figure BDA0002162772560000054
t is step (1)The key given in (1).
(11) And transforming the C into a matrix with the size of m multiplied by n, thereby obtaining a final ciphertext image.
3. A color image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation is provided.
(1) The color image is decomposed into three components of R, G and B, the hash value of each component is calculated, and the system initial value used by the 2D-HCMM in the encryption process of each component is updated.
(2) And generating random sequences corresponding to the components through the 2D-HCMM, and encrypting the three components of R, G and B respectively by using a content 2 method.
(3) And synthesizing the results of the three components after encryption into a final ciphertext image.
Drawings
FIG. 1 is a flow chart of the present invention
Detailed Description
The invention provides an image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping and gene operation, which mainly comprises the following five steps:
generating a random sequence;
(II) gene recombination operation;
(III) performing gene mutation operation;
(IV) a row-column permutation operation;
and (V) integral diffusion operation.
The implementation platform is MATLAB and the operating system is win 10. The method comprises the following specific steps:
the first step is as follows: generating random sequences
And calculating the hash value of the plaintext image, and updating the initial value of the chaotic system. According to a given system parameter (secret key) and an updated initial value, iterating the 2D-HCMM chaotic system, and then preprocessing a generated random sequence to obtain the random sequence used in the encryption process.
The second step is that: operation of Gene recombination
And extracting 8 bit planes of the plaintext image, and sequentially selecting two of the bit planes to combine to form four composite bit planes. The four bit planes are recombined, the high correlation among the planes is disturbed, and four new composite bit planes are obtained.
The third step: manipulation of genetic variation
And (4) carrying out two rounds of variation on the bit plane recombined in the second step according to the random sequence generated in the first step, thereby achieving the purpose of randomly changing the pixel value.
The fourth step: rank permute operation
And synthesizing the four bit planes subjected to mutation into an eight-bit image, and performing line replacement on the eight-bit image. And after the row replacement is finished, performing column replacement on the image, and fully disordering the positions of the original pixels.
The fifth step: bulk diffusion operation
And (3) converting the scrambled image into a sequence, carrying out XOR operation on one pixel in the sequence, one value of the random sequence and the previous ciphertext pixel each time, and sequentially iterating to finally achieve the effect of overall diffusion to obtain the final ciphertext image.

Claims (4)

1. The image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping and gene operation is characterized by comprising the following steps of:
(1) a new two-dimensional Henon-Chebyshev chaotic system is provided;
(2) providing a gray level image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation;
(3) a color image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, gene recombination and gene variation is provided.
2. The new two-dimensional Henon-Chebyshev chaotic system (2D-HCMM) according to claim 1, characterized in that: by analyzing the phase diagram, the bifurcation diagram, the Lyapunov exponent and the information entropy, the 2D-HCMM has a better dynamic structure, better ergodicity and unpredictability than the original Henon mapping and Chebyshev mapping, and the chaos range of the 2D-HCMM is expanded. The chaos range of the 2D-HCMM is a, c belongs to R,
Figure FDA0002162772550000011
and the larger the absolute value of b is, the better the chaotic behavior is.
3. The gray scale image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, genetic recombination and genetic variation as claimed in claim 1, characterized in that: the random sequence used at each stage in the encryption process is generated by the 2D-HCMM. The initial value of the 2D-HCMM and the system parameters are used as a key, and the initial value is updated according to the hash value of the plaintext image during encryption. Genetic recombination operations are mainly used to perturb the high correlation of the bit planes, genetic variations aim at randomly changing the value of the bit levels to achieve pixel-level diffusion. In addition, conventional encryption structures are also used in encryption processes, such as row-column permutation and global diffusion. The method can resist various classical types of attacks, has quite high execution speed, and realizes good balance between safety and efficiency.
4. The color image encryption method based on two-dimensional Henon-Chebyshev chaotic mapping, genetic recombination and genetic variation as claimed in claim 1, characterized in that: the color image is decomposed into three components of R, G and B, the hash value of each component is calculated, and the system initial value used by the 2D-HCMM in the encryption process of each component is updated. And generating random sequences corresponding to the components through the 2D-HCMM, and encrypting the three components of R, G and B respectively by using a content 2 method. And synthesizing the results of the three components after encryption into a final ciphertext image.
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CN117439730B (en) * 2023-12-20 2024-02-20 湖南省第三测绘院 Geographic information encryption method, system and medium based on Chaos-LSTM and chaotic sequence proliferation

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